Actresses including Oscar-nominated Carey Mulligan have expressed interest in playing Lisbeth Salander, a computer hacker recruited by a journalist to find a woman who has been missing for 40 years. That part has not yet been cast, and other actresses including Keira Knightley and Natalie Portman have also expressed interest.

Craig would play journalist Mikael Blomkvist who is looking for the missing woman, Harriet Banger.

A Sony spokesman said, "We have not offered any roles to anyone nor are we negotiating with anyone."

While Brad Pitt has been reportedly considering the lead role, an individual close to the negotiations said that Craig was close to a deal. The James Bond star will fly out to Los Angeles on Friday to have dinner with Fincher, who’s slated to direct the three-picture franchise for Sony.

The movie will shoot in October, and is slated for release in December 2011.

Larsson’s "Millennium Trilogy," which includes "The Girl With The Dragon Tattoo," "The Girl Who Played With Fire," and "The Girl Who Kicked The Hornets’ Nest," has sold over 25 million copies around the world.

A Danish film adaptation of "Girl With The Dragon Tattoo" was released last year and has been playing internationally.

Negotiations between Craig and Sony aren’t entirely finished, but TheWrap was told he’s extremely close to signing. Brad Pitt was also reportedly considering the role.

Craig begins shooting on Jon Favreau‘s "Cowboys & Aliens" next week. "Girl With The Dragon Tattoo" would be his next movie.